D. Ambrosi and L. Preziosi, ON THE CLOSURE OF MASS BALANCE MODELS FOR TUMOR GROWTH, Mathematical Models and Methods in Applied Sciences, vol.12, issue.05, pp.737-754, 2002.
DOI : 10.1080/10273669908833027

M. Bissell and W. Hines, Why don't we get more cancer? A proposed role of the microenvironment in restraining cancer progression, Nature Medicine, vol.23, issue.3, pp.320-329, 2011.
DOI : 10.1200/JCO.2005.11.030

D. Bresch, T. Colin, E. Grenier, B. Ribba, and O. Saut, A viscoelastic model for avascular tumor growth. Discrete and continuous dynamical systems, supplement, pp.101-108, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00267292

D. Bresch, T. Colin, E. Grenier, B. Ribba, and O. Saut, Computational Modeling of Solid Tumor Growth: The Avascular Stage, SIAM Journal on Scientific Computing, vol.32, issue.4, pp.2321-2344, 2010.
DOI : 10.1137/070708895
URL : https://hal.archives-ouvertes.fr/inria-00148610

O. Brummer, S. Athar, L. Riethdorf, T. Löning, and H. Herbst, Matrix-metalloproteinases 1, 2 and 3 and their tissue inhibitors 1 and 2 in benign and malignant breast lesions: an in situ hybridization study, Virchows Archiv, vol.435, issue.6, pp.566-573, 1999.
DOI : 10.1007/s004280050442

M. Cichon, A. Degnim, D. Visscher, and D. Radisky, Microenvironmental Influences that Drive Progression from Benign Breast Disease to Invasive Breast Cancer, Journal of Mammary Gland Biology and Neoplasia, vol.101, issue.14, pp.389-397, 2010.
DOI : 10.4161/cc.4.8.1903
URL : https://link.springer.com/content/pdf/10.1007%2Fs10911-010-9195-8.pdf

M. Duffy, T. Maguire, A. Hill, and E. Mcdermott, Metalloproteinases: role in breast carcinogenesis, invasion and metastasis, Breast Cancer Research, vol.91, issue.4, pp.252-257, 2000.
DOI : 10.1093/jnci/91.19.1678
URL : https://breast-cancer-research.biomedcentral.com/track/pdf/10.1186/bcr65?site=breast-cancer-research.biomedcentral.com

R. P. Fedkiw, T. Aslam, B. Merriman, and S. Osher, A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method), Journal of Computational Physics, vol.152, issue.2, pp.457-492, 1999.
DOI : 10.1006/jcph.1999.6236

A. S. For and C. Biology, Externally applied forces can phenotypically revert malignant breast epithelial structures, ASCB, 2012 annual meeting abstracts, 2012.

S. Franks, H. Byrne, J. King, J. Underwood, and C. Lewis, Modelling the early growth of ductal carcinoma in situ of the breast, Journal of Mathematical Biology, vol.47, issue.5, pp.424-452, 2003.
DOI : 10.1007/s00285-003-0214-x

S. Franks, H. Byrne, J. Mudhar, J. Underwood, and C. Lewis, Mathematical modelling of comedo ductal carcinoma in situ of the breast, Mathematical Medicine and Biology, vol.20, issue.3, pp.277-308, 2003.
DOI : 10.1093/imammb/20.3.277

O. Gallinato, M. Ohta, C. Poignard, and T. Suzuki, Free boundary problem for cell protrusion formations: theoretical and numerical aspects, Journal of Mathematical Biology, vol.18, issue.1, 2016.
DOI : 10.2977/prims/1195184016
URL : https://hal.archives-ouvertes.fr/hal-01228013

O. Gallinato and C. Poignard, Superconvergent second order Cartesian method for solving free boundary problem for invadopodia formation, Journal of Computational Physics, vol.339, 2016.
DOI : 10.1016/j.jcp.2017.03.010
URL : https://hal.archives-ouvertes.fr/hal-01483484

H. Greenspan, On the growth and stability of cell cultures and solid tumors, Journal of Theoretical Biology, vol.56, issue.1, pp.229-242, 1976.
DOI : 10.1016/S0022-5193(76)80054-9

A. Hama¨?hama¨?, J. Muret, A. Cavalcanti, S. Bonvalot, and S. Choua¨?bchoua¨?b, Le facteur de nécrose tumorale : de la biologièbiologiè a la thérapie oncologique, Hématologie, vol.15, issue.4, pp.291-304, 2009.

M. Hu and K. Polyak, Microenvironmental regulation of cancer development, Current Opinion in Genetics & Development, vol.18, issue.1, pp.27-34, 2008.
DOI : 10.1016/j.gde.2007.12.006

M. Hu, J. Yao, D. Carroll, S. Weremowicz, H. Chen et al., Regulation of In Situ to Invasive Breast Carcinoma Transition, Cancer Cell, vol.13, issue.5, pp.394-406, 2008.
DOI : 10.1016/j.ccr.2008.03.007

O. Kavian, M. Legù-ebe, C. Poignard, and L. Weynans, ???Classical??? Electropermeabilization Modeling at the Cell Scale, Journal of Mathematical Biology, vol.1724, issue.4, pp.235-265, 2014.
DOI : 10.1016/j.bbagen.2005.05.006
URL : https://hal.inria.fr/hal-00712683/document

K. Kellner, G. Liebsch, I. Klimant, O. S. Wolfbeis, T. Blunk et al., Determination of oxygen gradients in engineered tissue using a fluorescent sensor, Biotechnology and Bioengineering, vol.1221, issue.1, pp.73-83, 2002.
DOI : 10.1016/0167-4889(94)90210-0

Y. Kim and H. G. Othmer, A Hybrid Model of Tumor???Stromal Interactions in Breast Cancer, Bulletin of Mathematical Biology, vol.7, issue.492, pp.1304-1350, 2013.
DOI : 10.1111/j.1440-1681.1993.tb01697.x

Y. Kim, M. Stolarska, and H. Othmer, The role of the microenvironment in tumor growth and invasion, Progress in Biophysics and Molecular Biology, vol.106, issue.2, pp.353-379, 2011.
DOI : 10.1016/j.pbiomolbio.2011.06.006

F. Kleinhans, Membrane Permeability Modeling: Kedem???Katchalsky vs a Two-Parameter Formalism, Cryobiology, vol.37, issue.4, pp.271-289, 1998.
DOI : 10.1006/cryo.1998.2135

A. Köhrmann, U. Kammerer, M. Kapp, J. Dietl, and J. Anacker, Expression of matrix metalloproteinases (MMPs) in primary human breast cancer and breast cancer cell lines: New findings and review of the literature, BMC Cancer, vol.99, issue.6, p.188, 2009.
DOI : 10.1002/ijc.10329

G. Lefebvre, F. Cornelis, P. Cumsille, T. Colin, C. Poignard et al., Spatial modelling of tumour drug resistance: the case of gist liver metastases, Mathematical Medicine and Biology, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01380292

M. Legù-ebe, A. Silve, L. Mir, and C. Poignard, Conducting and permeable states of cell membrane submitted to high voltage pulses: Mathematical and numerical studies validated by the experiments, Journal of Theoretical Biology, vol.360, pp.83-94, 2014.
DOI : 10.1016/j.jtbi.2014.06.027

P. Macklin, M. Edgerton, A. Thompson, and V. Cristini, Patient-calibrated agent-based modelling of ductal carcinoma in situ (DCIS): From microscopic measurements to macroscopic predictions of clinical progression, Journal of Theoretical Biology, vol.301, pp.122-140, 2012.
DOI : 10.1016/j.jtbi.2012.02.002

K. Norton, M. Wininger, G. Bhanot, S. Ganesan, N. Barnard et al., A 2D mechanistic model of breast ductal carcinoma in situ (DCIS) morphology and progression, Journal of Theoretical Biology, vol.263, issue.4, pp.393-406, 2010.
DOI : 10.1016/j.jtbi.2009.11.024

C. Overall and C. López-otín, Strategies for mmp inhibition in cancer: innovations for the post-trial era, Nature Reviews Cancer, vol.2, issue.9, pp.657-672, 2002.
DOI : 10.1038/nrc884

R. Perrussel and C. Poignard, Asymptotic expansion of steady-state potential in a high contrast medium with a thin resistive layer, Applied Mathematics and Computation, vol.221, pp.48-65, 2013.
DOI : 10.1016/j.amc.2013.06.047
URL : https://hal.archives-ouvertes.fr/inria-00442659

R. Poincloux, F. Lizárraga, and P. Chavrier, Matrix invasion by tumour cells: a focus on MT1-MMP trafficking to invadopodia, Journal of Cell Science, vol.122, issue.17, pp.3015-3024, 2009.
DOI : 10.1242/jcs.034561

D. Ramsay, J. Kent, R. Hartmann, and P. Hartmann, Anatomy of the lactating human breast redefined with ultrasound imaging, Journal of Anatomy, vol.2, issue.4, pp.525-534, 2005.
DOI : 10.1148/radiology.196.1.7784555

S. Rha, J. Kim, J. Roh, K. Lee, J. Min et al., Sequential production and activation of matrix- metalloproteinase-9 (MMP-9) with breast cancer progression, Breast Cancer Researsh and Treatment, vol.43, pp.175-181, 1997.

B. Ribba, O. Saut, T. Colin, D. Bresh, E. Grenier et al., A multiscale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents, Journal of Theoretical Biology, vol.243, issue.4, pp.532-541, 2006.
DOI : 10.1016/j.jtbi.2006.07.013
URL : https://hal.archives-ouvertes.fr/inria-00332464

R. Sakr, Carcinomes canalaires in situ du sein??: r??le potentiel de la biologie mol??culaire, Gyn??cologie Obst??trique & Fertilit??, vol.41, issue.1, pp.45-53, 2012.
DOI : 10.1016/j.gyobfe.2012.11.004

J. S. Sartakhti, M. H. Manshaei, and M. Sadeghi, MMP???TIMP interactions in cancer invasion: An evolutionary game-theoretical framework, Journal of Theoretical Biology, vol.412, 2016.
DOI : 10.1016/j.jtbi.2016.09.019

J. A. Sethian, Fast Marching Methods, SIAM Review, vol.41, issue.2, pp.199-235, 1999.
DOI : 10.1137/S0036144598347059

J. Tse, G. Cheng, J. Tyrrell, S. Wilcox-adelman, Y. Boucher et al., Mechanical compression drives cancer cells toward invasive phenotype, Proceedings of the National Academy of Sciences, vol.20, issue.1, pp.911-916, 2012.
DOI : 10.1039/B613349E
URL : http://www.pnas.org/content/109/3/911.full.pdf

A. Waterston and M. Bower, TNF and cancer : good or bad ? Cancer Therapy, pp.131-148, 2004.

V. Weaver, A. Fisher, O. Peterson, and M. Bissell, The importance of the microenvironment in breast cancer progression: recapitulation of mammary tumorigenesis using a unique human mammary epithelial cell model and a three-dimensional culture assay, Biochemistry and Cell Biology, vol.74, issue.6, pp.833-851, 1996.
DOI : 10.1139/o96-089

S. Yang, To revert breast cancer cells, give them the squeeze, 2012.